You can record that a student earned a certificate in ASAP by going to Class Details | Grades/Credits and marking the Pass/Completed button.
Be sure to click Save at the bottom of the page.
Also, please note there is a Preference you can set which changes the student's enrollment status to Completed automatically upon checking the Pass/Completed button and saving. See Configure | Preferences | Public Site | Change Enroll Status on pass/completed and change to "Yes" or checked.